Equidistribution of phase shifts in semiclassical potential scattering

@article{GellRedman2015EquidistributionOP,
  title={Equidistribution of phase shifts in semiclassical potential scattering},
  author={Jesse Gell-Redman and Andrew Hassell and Steve Zelditch},
  journal={J. London Math. Society},
  year={2015},
  volume={91},
  pages={159-179}
}
Consider a semiclassical Hamiltonian H := h2∆ + V − E where ∆ is the positive Laplacian on Rd, V ∈ C∞ 0 (Rd) and E > 0 is an energy level. We prove that under an appropriate dynamical hypothesis on the Hamilton flow corresponding to H, the eigenvalues of the scattering matrix Sh(V ) define a measure on S1 that converges to Lebesgue measure away from 1 ∈ S1 as h→ 0.